This application claims the benefit of Korean Application Nos. 2001-10916 and 2001-10917, both filed Mar. 2, 2001, in the Korean Patent Office, the disclosures of which are incorporated herein by reference.
1. Field of the Invention
The present invention relates to a micromirror driver, and more particularly, to a micromirror driver which controls a resonant frequency and an amplitude of a micromirror as the micromirror rotates due to electrostatic forces, and increases a rotation angle of the micromirror using a lower voltage, and to a method of controlling the micromirror driver.
2. Description of the Related Art
micromirror drivers are operated by electrostatic forces and switch a path, along which light beams are reflected, using a rotation angle of a micromirror.
Referring to FIG. 1, a conventional micromirror driver comprises a frame 5, a trench 10 formed in the frame 5, a micromirror 20 received in the trench 10 and having a base electrode 15, a torsion spring 25 which supports the micromirror 20 in rotation, and an electrode 30 which interacts with the base electrode 15 to rotate the micromirror 20 .
The micromirror 20 rotates about the torsion spring 25 due to electrostatic forces generated between the base electrode 15 and the electrode 30, as shown in FIG. 2. If the micromirror sufficiently rotates with a predetermined rotation angle, the micromirror 20 is restored to a horizontal state due to elastic restoring forces of the torsion spring 25. The micromirror 20 repeatedly rotates in the above-described manner. It is possible to allow a rotating body, such as the micromirror 20, to rotate with a greater rotation angle with a use of less voltage, taking advantage of resonance characteristics of an oscillating body. In other words, it is possible to effectively operate an oscillating body with less driving forces if the oscillating body is operated with a frequency, which is the same as a resonant frequency of the oscillating body.
A conventional method of adjusting the resonant frequency of a micromirror increases or decreases a mass of the micromirror and a spring constant of a torsion spring. However, such a mass of the micromirror and the spring constant of a torsion spring are set in accordance with manufacturing conditions and may vary according to an environment, in which the micromirror is manufactured or is driven. Accordingly, it is difficult to obtain a precise resonant frequency of the micromirror due to variations in the manufacture of the micromirror. Thus, various efforts have been made to control the resonant frequency of a micromirror after manufacturing the micromirror.
The resonant frequency f of an oscillating body can be expressed by Equation (1).                     f        =                              1                          2              ⁢              π                                ⁢                                                    K                t                            I                                                          (        1        )            
In Equation (1), Kt represents a spring constant, and I represents an inertia moment.
The equation of motion concerning the micromirror 20 rotating with a predetermined rotation angle (xcex8) is shown below as Equation (2).                                                                                           I                  ⁢                                      xe2x80x83                                    ⁢                                      θ                    ¨                                                  +                                                      C                    t                                    ⁢                                      θ                    .                                                  +                                                      K                    t                                    ⁢                  θ                                            =                            ⁢                              τ                ⁡                                  (                                      θ                    ,                    V                                    )                                                                                                        =                            ⁢                                                1                  2                                ⁢                                  ⅆ                                      ⅆ                    θ                                                  ⁢                                  (                                      CV                    2                                    )                                                                                        (        2        )            
In Equation (2), I represents an inertia moment, Ct represents capacitance between the base electrode 15 of the micromirror 20 and the electrode 30, Kt represents the spring constant of the torsion spring 25, and xcfx84 represents a rotation moment (torque). Where V0, xcex1, and V represent an initial voltage of the electrode 30, an arbitrary coefficient and a driving voltage of the electrode 30, respectively, and V=(V0+xcex1xcex8), Equation (2) can be rearranged into Equation (3)                                                                                           I                  ⁢                                      xe2x80x83                                    ⁢                                      θ                    ¨                                                  +                                                      C                    t                                    ⁢                                      θ                    .                                                  +                                                      K                    t                                    ⁢                  θ                                            =                            ⁢                                                                    1                    2                                    ⁢                                                            ⅆ                      C                                                              ⅆ                      θ                                                        ⁢                                      V                    2                                                  +                                                      1                    2                                    ⁢                                      C                    ⁡                                          (                                              2                        ⁢                        V                                            )                                                        ⁢                                                            ⅆ                      V                                                              ⅆ                      θ                                                                                                                                              =                            ⁢                                                                    1                    2                                    ⁢                                                            ⅆ                      C                                                              ⅆ                      θ                                                        ⁢                                      (                                                                  V                        0                        2                                            +                                              2                        ⁢                                                  V                          0                                                ⁢                        αθ                                            +                                                                        a                          2                                                ⁢                                                  θ                          2                                                                                      )                                                  +                                                      1                    2                                    ⁢                                      C2                    ⁡                                          (                                                                        V                          0                                                +                                                  α                          ⁢                                                      xe2x80x83                                                    ⁢                          θ                                                                    )                                                        ⁢                  α                                                                                        (        3        )            
by substitution of V=(V0+xcex1xcex8).
The capacitance Ct is linearly varied with respect to the rotation angle xcex8 of the micromirror 20, as shown in FIG. 3. In other words, as the rotation angle xcex8 of the micromirror 20 increases, the distance between the base electrode 15 and the electrode 30 increases, and thus the capacitance Ct linearly decreases. Accordingly, a variation of the capacitance Ct with respect to a variation of the rotation angle xcex8 becomes a constant xcex3.
The constant xcex3 can be expressed as             ⅆ      C              ⅆ      θ        =      γ    .  
Accordingly, C=C0+xcex3xcex8 where C0 represents a capacitance value when xcex8=0. Equation (3) can be rearranged into Equation (4) by substitutions of             ⅆ      C              ⅆ      θ        =  γ
and C=C0+xcex3xcex8.                                           I            ⁢                          xe2x80x83                        ⁢                          θ              ¨                                ⁢                      xe2x80x83                    +                                    C              t                        ⁢                          θ              .                                +                                    K              t                        ⁢            θ                          =                              1            2                    ⁡                      [                                                            (                                                            γ                      ⁢                                              xe2x80x83                                            ⁢                                              V                        0                                                              +                                          2                      ⁢                                              αC                        0                                                                              )                                ⁢                                  V                  0                                            +                                                (                                                            4                      ⁢                      γ                      ⁢                                              xe2x80x83                                            ⁢                      α                      ⁢                                              xe2x80x83                                            ⁢                                              V                        0                                                              +                                          2                      ⁢                                              α                        2                                            ⁢                                              C                        0                                                                              )                                ⁢                θ                            +                              3                ⁢                                  γα                  2                                ⁢                                  θ                  2                                                      ]                                              (        4        )            
In the right side of Equation (4), (xcex3V0+2xcex1C0) affects the rotation amplitude of the micromirror 20, (4xcex3xcex1V0+2xcex12C0) affects the resonant frequency ƒ of the micromirror 20, and 3xcex3xcex12 affects both the amplitude and the resonant frequency of the micromirror 20. Here, if the resonant frequency ƒ of the micromirror 20 is controlled by adjusting xcex1, the voltage V of the driving voltage of the electrode 30 is varied because V=(V0+xcex1xcex8). If the initial voltage V0 of the electrode 30 is varied, xcex1 is also varied. Thus, it is impossible to simultaneously control the frequency ƒ and the amplitude of the micromirror 20. In other words, elements required to control the frequency ƒ and the amplitude of the micromirror 20 are dependent on each other, and thus if one of the elements is controlled, the other element is affected by the controlled element and cannot be controlled simultaneously or independently.
To solve the above-described problems, it is an object of the present invention to provide a micromirror driver, in which a frequency controlling electrode and an amplitude controlling electrode operate independently and thus a resonant frequency and an amplitude of a micromirror are independently and simultaneously controllable, allowing the micromirror to rotate with a larger rotation angle by decreasing a spring constant of a rotation axis of the micromirror. Another object of the present invention is to provide a method of controlling a micromirror driver.
Additional objects and advantages of the invention will be set forth in part in the description which follows, and, in part, will be obvious from the description, or may be learned by practice of the invention.
Accordingly, to achieve the above and other objects of the invention, according to one aspect of the present invention, there is provided a micromirror driver. The micromirror driver comprises a micromirror having at least one groove, an elastic body which supports the micromirror in rotation, and at least one electrode which receives a voltage to generate electrostatic forces to rotate the micromirror through interaction of the electrostatic forces with the micromirror. The amplitude and frequency of the micromirror are controlled by varying one of a magnitude and a waveform of the voltage of the at least one electrode.
Each groove is formed in a respective peripheral area of the micromirror and is arranged near a rotation axis of the micromirror.
Preferably, a first electrode controls the frequency of the micromirror during rotation of the micromirror, a second electrode controls the amplitude of the micromirror during the rotation of the micromirror, and the second electrode operates independently of the first electrode.
A voltage V of the at least one electrode satisfies the equation, V2=V0+xcex1xcex8, where V0 represents an initial voltage of the at least one electrode, xcex1 represents an arbitrary coefficient, and xcex8 represents a rotation angle of the micromirror. A voltage V1 of the first electrode satisfies the equation, V12=V0, and a voltage V2 of the second electrode satisfies the equation, V22=V0.
A base electrode is formed on the micromirror and the base electrode and the first and second electrodes are formed in a comb shape and the combs of the first and second electrodes and the comb of the base electrode are arranged gear-like so that an effective area of opposing surfaces of the electrodes is maximized.
Preferably, a plurality of grooves are formed in the micromirror and arranged symmetrically with respect to the rotation axis of the micromirror.
In order to achieve the above and other objects of the present invention, according to another aspect of the present invention, there is provided a micromirror driver. The micromirror driver comprises a micromirror having at least one groove and a base electrode formed at the groove, an elastic body which supports the micromirror in rotation, and at least two electrodes which drive the micromirror in rotation by generating electrostatic forces through interaction of the at least two electrodes with the base electrode and, the at least two electrodes operating independently of each other.
One of the at least two electrodes is used to control the frequency of the micromirror by varying a waveform of a voltage applied to the one electrode.
The other of the at least two electrodes is used to control the amplitude of the micromirror by varying the magnitude of the voltage applied to the other of the at least two electrodes.
In order to achieve the above and other objects of the present invention, according to another aspect of the present invention, there is provided a method of controlling a micromirror driver, which comprises a micromirror, an elastic body supporting the micromirror in rotation, and at least one electrode. The method comprises: generating electrostatic forces between the micromirror and the at least one electrode; a voltage V of the at least one electrode to satisfy an equation, V2=V0+xcex1xcex8 where V0 represents an initial voltage of the at least one electrode, xcex1 represents an arbitrary coefficient, and xcex8 represents a rotation angle of the micromirror, and controlling a frequency and/or an amplitude of the micromirror by varying the initial voltage V0 of the at least one electrode and the arbitrary coefficient xcex1.
Preferably, a second electrode controls a resonant frequency ƒ of the micromirror by varying the arbitrary coefficient xcex1 in an equation, V2=xcex1xcex8, and the resonant frequency ƒ of the micromirror is expressed by the equation,   f  =            1              2        ⁢        π              ⁢                                        K            t                    -                                    γ              2                        ⁢            α                          I            
wherein Kt represents the spring constant of the elastic body, I represents an inertia moment of the micromirror, and xcex32 represents a variation of capacitance with respect to a variation of the rotation angle xcex8 of the micromirror.
The second electrode controls the resonant frequency ƒ of the micromirror by varying the arbitrary coefficient xcex1 in the equation, V2=xcex1xcex8, and in a case where a voltage with a phase difference of xcfx80/2 is applied to the first and second electrodes, the resonant frequency ƒ of the micromirror can be expressed by the equation,   f  =            1              2        ⁢        π              ⁢                                        K            t                    +                                    γ              2                        ⁢            α                          I            
wherein Kt represents the spring constant of the elastic body, I represents the inertia moment of the micromirror, and xcex32 represents a variation of capacitance with respect to a variation of the rotation angle xcex8 of the micromirror.
In order to achieve the above and other objects, according to another aspect of the present invention, there is provided a method of controlling a micromirror driver, which comprises a micromirror, an elastic body supporting the micromirror in rotation, and at least one electrode which rotates the micromirror by generating electrostatic forces through interaction with the micromirror. The method includes the step of comprising controlling the resonant frequency of the micromirror by varying the waveform of the driving voltage of the at least one electrode.